Given a biobjective linearprogramming problem,we develop an affine scaling algorithm with min-max direction and demonstrate its convergence for an efficient *** implement the algorithm for some minor issues in the li...
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Given a biobjective linearprogramming problem,we develop an affine scaling algorithm with min-max direction and demonstrate its convergence for an efficient *** implement the algorithm for some minor issues in the literature.
This work offers an integrated methodological framework for decision support in planning the implementation of measures that address the barriers to university technology transfer (UTT). The planning problem consists ...
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This work offers an integrated methodological framework for decision support in planning the implementation of measures that address the barriers to university technology transfer (UTT). The planning problem consists of two parts: 1) identifying the high priority measures;2) optimally implementing these measures over a specified planning horizon subject to resource constraints. Treated as a multi-criteria sorting problem under uncertainty, the high priority measures are determined via fuzzy DEcision MAking Trial and Evaluation Laboratory (DEMATEL) and analytic network process (ANP) for evaluating the barriers, and the fuzzy FlowSort (F-FlowSort) for classifying the priority of the various measures. Then, an extended multi-objective extension of the Preference Ranking Organization METHod for Enrichment Evaluations V (PROMETHEE V) is offered to determine the degree of implementation of the high priority measures over multiple periods. Demonstrated in an actual case study with 29 identified measures under 24 previously known barriers, findings reveal six high priority measures, which include designing a sustained partnership, engaging in joint research ventures, establishing partnerships from international financial institutions, streamlining objectives to full support of the technology readiness levels, establishing a holistic system approach towards technology readiness levels, and establishing agreements to have access to the industry laboratory facilities. The implementation plan, represented as a set of Pareto optimal solutions, is obtained through the augmented epsilon -constraint (AUGMECON) algorithm for the epsilon -constrained multi-objective linearprogramming formulation of the extended PROMETHEE V. Layers of sensitivity analysis were performed to test the robustness of the results to changes in the parameters. Finally, policy insights are provided to key decision-makers for advancing UTT.
We propose a modelling framework which allows considering different priorities and individual expansion and contraction scales for distinct types of inputs and outputs, through the Weighted Russell Directional Distanc...
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We propose a modelling framework which allows considering different priorities and individual expansion and contraction scales for distinct types of inputs and outputs, through the Weighted Russell Directional Distance Model (WRDDM). An equivalence model between the WRDDM and the super-ideal point model has also been established, which is then incorporated into several interactive multiobjective linear programming (MOLP) approaches. The use of these diverse interactive methodologies allows obtaining the benchmark Decision Making Units (DMUs) which best suit the decision maker's (DM) preferences. This feature can be useful since traditional Data Envelopment Analysis (DEA) models tend to completely neglect the DM's preferences and value judgements in the computation of the DMUs used as a reference of best practices. Therefore, with this tool the DMs have the possibility of translating into the decision-making process management constraints (namely, budgetary) and aspiration levels regarding the inputs and outputs, providing much more realistic support for actual decision-making.
multiobjectivelinear optimization problems (MOLPs) arise when several linear objective functions have to be optimized over a convex polyhedron. In this paper, we propose a new method for generating the entire efficie...
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multiobjectivelinear optimization problems (MOLPs) arise when several linear objective functions have to be optimized over a convex polyhedron. In this paper, we propose a new method for generating the entire efficient set for MOLPs in the outcome space. This method is based on the concept of adjacencies between efficient extreme points. It uses a local exploration approach to generate simultaneously efficient extreme points and maximal efficient faces. We therefore define an efficient face as the combination of adjacent efficient extreme points that define its border. We propose to use an iterative simplex pivoting algorithm to find adjacent efficient extreme points. Concurrently, maximal efficient faces are generated by testing relative interior points. The proposed method is constructive such that each extreme point, while searching for incident faces, can transmit some local informations to its adjacent efficient extreme points in order to complete the faces' construction. The performance of our method is reported and the computational results based on randomly generated MOLPs are discussed. (C) 2012 Elsevier Inc. All rights reserved.
We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x...
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We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x* is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the case of only one objective. Provided that x* is a non-degenerate basic solution, the problem is polynomially solvable for one objective, but remains co-NP-hard in the general case. Some open problems are mentioned at the end of the paper.
This paper deals with a class of biobjective mixed binary linear programs having a multiple-choice constraint, which are found in applications such as Pareto set-reduction problems, single-supplier selection, and inve...
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This paper deals with a class of biobjective mixed binary linear programs having a multiple-choice constraint, which are found in applications such as Pareto set-reduction problems, single-supplier selection, and investment decisions, among others. Two objective space-search algorithms are presented. The first algorithm, termed line search and linearprogramming filtering, is a two-phase procedure. Phase 1 searches for supported Pareto outcomes using the parametric weighted sum method, and Phase 2 searches for unsupported Pareto outcomes by solving a sequence of auxiliary mixed binary linear programs. An effective linearprogramming filtering procedure excludes arty previous outcomes found to be dominated. The second algorithm, termed linearprogramming decomposition and filtering, decomposes the mixed binary problem by iteratively fixing binary variables and uses the linearprogramming filtering procedure to prune out any dominated outcomes. Computational experiments show the effectiveness of the linearprogramming filtering and suggest that both algorithms run faster than existing general-purpose objective space-search procedures.
Aggregate production planning (APP) is a significant level that seeks efficient production systems. In actual condition, APP decisions, production inputs, and relevant planning parameters are intrinsically imprecise, ...
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Aggregate production planning (APP) is a significant level that seeks efficient production systems. In actual condition, APP decisions, production inputs, and relevant planning parameters are intrinsically imprecise, which results in significant complexities in the generation of master production schedules. Thus, this paper proposes a hybridization of a fuzzy programming, simulated annealing (SA), and simplex downhill (SD) algorithm called fuzzy-SASD to establish multiple-objective linearprogramming models and consequently resolve APP problems in a fuzzy environment. The proposed strategy is dependent on Zimmerman's approach for handling all inexact operating costs, data capacities, and demand variables. The SD algorithm is employed to balance exploitation and exploration in SA, thereby efficient and effective (speed and quality) solution for the APP model. The proposed approach produces rates for efficient solutions of APP in large-scale problems that are 33, 83, and 89% more efficient than those of particle swarm optimization (PSO), standard algorithm (SA), and genetic algorithm (GA), respectively. Moreover, the proposed approach produces a significantly low average rate for computational time at only 64, 77, and 24% compared with those of GA, PSO, and SA, respectively. Experimental results indicate that the fuzzy-SASD is the most effectual of all approaches.
It is well-known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for...
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It is well-known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top-down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top-down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.
Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present...
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Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal (Math Program 141(1-2): 103-120, 2013) on quasi-concave problems and Shao and Ehrgott (Optimization 65(2): 415-431, 2016) on multiplicative linear programs. Furthermore, it improves results of Lohne and Wagner (J Glob Optim 69(2): 369-385, 2017) on minimizing the difference f = g-h of two convex functions g, h where either g or h is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.
In this paper, we focus on multiobjective linear programming problems involving random variable coefficients in objective functions and constraints. Using the concept of chance constrained conditions, such multiobject...
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In this paper, we focus on multiobjective linear programming problems involving random variable coefficients in objective functions and constraints. Using the concept of chance constrained conditions, such multiobjective stochastic linearprogramming problems are transformed into deterministic ones based on the variance minimization model under expectation constraints. After introducing fuzzy goals to reflect the ambiguity of the decision maker's judgements for objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for them as a fusion of the stochastic programming and the fuzzy one. The application of the proposed method to an illustrative numerical example shows its usefulness.
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